Static reps are done by holding a weight in a fixed position, usually fully contracted, for an extended period of time. They are typically done for 1 or 2 reps only and the weight should be held for 15-25 seconds although the actual optimal time is still up for debate.

Statics are easier to do on certain exercises and more difficult on others. For example, flies, leg extentions, and side raises are great exercises to use statics on, but deadlifts or squats would be more difficult. On the compund exercises you would have to use substantially more weight than you use for regular reps. Statics also work great on pulldowns.

There are a few ways I use them. First, you can do a set to positive failure and once you cannot complete any more, have someone help you get the weight to a fully-contracted position and hold it up as long as you can. Then lower it under strict control until you have finished the rep.

You could also just pick a weight 20-40% heavier than your normal weight for that exercise and either use a cheat rep or have someone help you to get the weight in the fully contracted position. Then hold it as long as you can and lower it under control until the rep is completed. If you do them alone and not after a set of positive reps, you may want to so 2 static holds instead if one.

This is a great technique to use to blast through plateaus, but don't use it too often.

Mike Mentzer once told a story of a guy who was stuck at the same weight on his leg extensions for 2 complete cycles. Mentzer then had him perform static holds only for 2 or 3 workouts. When he went back to positive reps, his strength had increased and he was able to break through his plateau.